4. (a) Show that the following matrix is diagonalizable. (b) Find a matrix P that diagonalizes A. (c) Compute Alº with the help of the matrices P, P-1 and D where D = P-'AP, and check your result by computing A10 directly. -2 8 A = 0 -1

Q: It is possible for a 3 x 3 matrix A with eigenvalues 1 3,-3 + i, -2 + i.

A: Solve

Q: If 2 is one of the eigen vector of a matrix A = |1 ] A3x3 has three distinct eigen values then which…

A: INTRODUCTION: In linear algebra, eigenvalues are related to eigenvectors. In the analysis of linear…

Q: 1 is -1 2 An eigen vector of the matrix A = 4,

A:

Q: Suppose that A is 2x2 matrix with eigenvectors V, = which correspond to A, = 3, 12=2 respectively.…

A:

Q: Suppose A is a 6 x 6 matrix with eigenvalues A = 2, 2, 2, 2, –3, -3. (a): What is the determinant of…

A: Given: Suppose A is a 6x6 matrix with eigenvalues 2,2,2,2,-3,-3

Q: 2) does the following matrix is orthonormal and orthogonal? Why? R = 2

A: Orthogonal and orthonormal matrix

Q: the matrix has two eigen vector one (ارفق الاجابة)of this 32 2 0 0 -1 0 0 3 2

A:

Q: If A is 4 x 4 matrix with 4 linearly independent eigenvectors then A is diagonalizable. Select one:…

A: yes this is the fact If any matrix have same number of eigenvalues as his order then it is called…

Q: Which of the following matrices is not in Row Echelon Form (REF)?

A:

Q: If A and B are nxn matrices and v is an eigenvector of A with corresponding eigenvalue A and v is…

A:

Q: VýB × VA

A:

Q: 4. If we do not discuss orthogonal diagonalization, you may omit this problem. Let A be any m x n…

A:

Q: Calculate largest and smallest eigenvales of the given matrix by using power method and inverse…

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Q: If A is an orthogonal matrix, then it has a dominant eigenvalue. True False

A:

Q: -s of the matrix or p = 2. What the Eigen valu

A:

Q: Suppose A and B are nxn matrix and P is an invertible nxn matrix such that A = P-BP (a) Show that A™…

A: We will use Diagonalization  and proof of first part to find power of matrix

Q: 2. Consider the 6 x 8 matrix [1 3 0 0 0 0 1 0 2 0 5 -3 0 0 0 A 0 0 1 4 -7 -9 00 0 0 0 0 0 0 0 0 0 0…

A:

Q: If A is 3 x3 matrix with eigenvalues A= = 1,1,4 , then A is invertable. Select one: O True False

A:

Q: 4. Prove that the product of two upper triangular matrices is always another upper triangular…

A:

Q: If a 3x3 matrix has 3 distinct eigenvalues, then it is diagonalizable. O True O False

A: Given is  3*3 matrix

Q: 1 1 -1 6 A : -2 3 2 -4

A:

Q: If the eigen vectors of a 2 x 2 matrix A corresponding to the eiger -- 2 respectively then the…

A: The Eigen vector corresponding to Eigen value -1 is 11 The Eigen vector corresponding to Eigen value…

Q: If the diagonal matrix that is congruent to the given matrix is  2 0 0 0 -1 0 0 0 0 Can we…

A: Given matrix is A=−101011011. And the diagonal matrix that is congruent to the given matrix A is…

Q: In the LU decomposition of the matrix 4. if the diagonal elements of U are both 1, then 9. the lower…

A: Introduction :We have given a matrix , diagonal elements of the LU decomposition of this matrix are…

Q: The diagonal elements of a 3x3 matrix are 2, 1, -3 are respectively. If two of its eigen values are…

A:

Q: If A,B are n x n matrices , suppose  A and B have the same eigenvalues with n linearly independent…

A: Answer: True.

Q: If A is an orthogonal matrix, then it has a dominant eigenvalue. True O False

A:

Q: 2 Find the cosine of the angle between these two matrices, using the standard matrix inner product…

A: Solution

Q: For matrices A and B with B invertible AB and BA have the same eigenvalues.

A: soln:If A & B are two square matrices of order n then, AB & BA have same eigen values.Let A…

Q: If A is 3x3 matrix with eigenvalues A = 4,4,3 , then A is defective. Select one: O True O False

A: If A is 3×3 matrix . The eigenvalues are given as λ=4, 4, 3. Since the eigenvalues of the matrix A…

Q: If the matrix Anxn does not have n different eigenvalues, then it does not have n linearly…

A: Given statement is: If the matrix Am×n does not have n different eigen values, then it does not have…

Q: Is the following matrix diagonalizable? If so, provide the matrices P and D. If not, explain why not…

A:

Q: 2. By using Hadamard matrices of order 2 and 4, construct a Hadamard matrix of order 8.

A: Given: Let us construct a Hadamard matrix of order 8 using the Hadamard matrices of orders 2 and 4.

Q: Suppose A is a 4 x 4 matrix and B is a 4 x 2 matrix, and let uo, ..., U3 represent a sequence of…

A:

Q: Suppose that A is symmetric matrix which has eigenvalues -1, 0 and 1 and corresponding eigenvectors…

A: We have to determine a matrix P which orthogonally diagonalizes A and compute A100.

Q: 3) A = [3 Calculate the 10th power of the matrix with the Cayley-Hamilton Theorem.

A: Given:

Q: 7. Show that the matrix A=I– 2vv' , where v is a unit vector in R", and I is an nxn identity matrix,…

A:

Q: Next, let 1 = 3 to find the corresponding eigenspace. Similar to before, this is the null space of A…

A: I guess you are for the blanks where the boxes are given. I'm answering them in step to pls find.…

Q: If the square matrix A is invertible, then its eigenvalue cannot be zero.

A: True

Q: 1- the rank of the matrix A.

A:

Q: The diagonal elements of a 3x3 matrix are 2, 1, –3 are respectively. If two of its eigen values are…

A:

Q: If A is 3 x3 matrix with eigenvalues A = 4,4,3 , then A is defective. Select one: C True False

A: If A is 3 × 3 matrix with eigenvalues λ = 4, 4, 3  Then,  A is defective  We have to tell it is true…

Q: If A is 3 x 3 matrix with eigenvalues A = 4,4,3 , then A is defective. Select one: True False

A:

Q: If a real matrix , then the eigenvalues of AAT A is Ceal, always are false ! Trave symmetric matrix,…

A:

Q: For the matrix A, find (if possible) a nonsingular matrix P such that PAP Is diagonal. (If not…

A:

Q: 5. Show that the condition that the block matrices (8 ) m ( ) A 0 А С and B В can be matrices of the…

A: Given: The block matrices, A00B and AC0B.   To show: The given block matrices can be matrices of the…

Q: 2. Find the eigenvalues of the following matrix: 2x, = 9 -X, + 2x, -X, + 2x, x, = 8 3 Is the matrix…

A:

Q: Find an elementary matrix E that corresponds to the row operation of subtracting – 6 times Row 1…

A: Applying elementary row operation on identity matrix I we get the elementary matrix E.Now we find a…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.